CLASSIFICATION OF HARMONIC DISTORTIONS AS A FUNCTION OF ANGLE
(α
α) USING FUZZY CLASSIFICATION
IN FULL-BRIDGE, SINGLE-PHASE INVERTER AND ACTIVE FILTER
Ersen KURU
Leyla KURU
Electrical and Electronics Engineer
Ereğli Demir ve Çelik Fabrikaları T.A.Ş.
Kdz. Ereğli / ZONGULDAK
TURKEY
Abstract: In this article first of all normalized fundamentals
and harmonic voltage output and total harmonic distorsions as
a function of Angle (α) in full-bridge, single-phase inverters
are explained. Then fuzzy classification is explained. After, it is
explained how we can use the fuzzy classification to classify
harmonic distortion. So it is shown that we can classify
hormonic distortion level as a function of α using the fuzzy
classification technic. Finally, a new active filter control
scheme has been improved using fuzzy classification system
outputs and fundamental current I1. This research shows that
fuzzy classification approach can be successfully applied to
classify hormonic distortion level and active filter control
scheme.
Doç. Dr. Etem KÖKLÜKAYA
Dept. Of Electrical and Electronics Engineering
Sakarya University
Sakarya
TURKEY
This result in waveforms for VAN and VBN shown in
figure 2, where the waveform overlap angle α can be
controlled. During this overlap interval, the output
voltage is zero a consequence of either both top switches
or both bottom switches being on. With α=0, the output
waveform is similar to a square-wave inverter with the
maximum possible fundamental output magnitude [1].
I. Full-bridge, single-phase inverter control by
voltage cancellation
This type control is feasible only in a single-phase, full
bridge inverter circuit. It is based on the combination of
square-wave switching and PWM with a unipolar voltage
switching. In the circuit of figure 1, the switches in the
two inverter legs are controlled separately. But all
switches have a duty ratio of 0.5, similar to a squarewave control [1].
Figure 2. Waveforms of full bridge, single-phase inverter
It is easier to derive the fundamental and the harmonic
frequency components of the output voltage in terms of
Figure 1. Power circuit of full bridge, single-phase
inverter
1
β = 90 0 − α , as is shown in figure 2.
2
2
 ∧
 V0  =
 h π
2
=
π
π /2
∫ V0 cos(hθ ).dθ
−π / 2
β
∫V
d
. cos(hθ ).dθ
−β
4
 ∧
∴  V0  = Vd sin (hβ )
  h πh
where
1
β = 90 0 − α
2
and h is an odd integer.
Figure 3 shows the variation in the fundamentalfrequency component as well as the harmonic voltage as
a function of α. These are normalized with respect to the
fundamental-frequency components for the square-wawe
(α=0) operation . The total harmonic distortion, which is
the ratio of the rms value of the harmonic distortion to
the rms value of the fundamental-frequency component,
is also plotted as a function of α. Because of large
distortion, the curves are shown as dashed for large
values of α [1].
Major issue of concern in the electric power quality
industry is classification of power quality problems [2].
This article involves the development of several fuzzy
inference systems that accomplish the following
objective:
-
Identify and classify hormonic distortion level
as a function of α in full-bridge, single-phase
inverter using the fuzzy classification technic.
III. Fuzzy Classification of 3th, 5th and 7th
current harmonics
MATLAB Fuzzy Logic Toolbox is used for
identification and classification of fundamental and
harmonic voltage output and total harmonic distortion as
a function of α.
In the first part of this research, input variable α, output
variable 3th, 5th and 7th current harmonic levels are
defined. Membership functions (MF) are also defined for
input variable α, output variables 3th, 5th and 7th current
harmonics using figure 3. After defining the MF, we
defined fuzzy rules in MATLAB Fuzzy Logic Toolbox
Rule Editor. Finally fuzzy system is tested using different
α values. Figure 4 shows the complete classification
algorithm we proposed.
α
Figure 3. Normalized fundamental and harmonic voltage
output and total harmonic distortion as a function of α
II. Fuzzy Classification
Fuzzy logic is an attempt at the representation and
utilization of knowledge but in a way more comparable
to the way humans think. “Crisp” variables and crisp
knowledge are elements in the knowledge-domain that
have an exat “truth value” ; either TRUE or FALSE.
Another definition of fuzzy logic is that it is a method for
easily representing analog processes on a digital
computer. These processes are concerned with
continuous phenomena that are not easily broken down
into discrete segments, and the concepts involved are
difficult to model along mathematical or rule-based lines
[3-4]
İnput variable
Fuzzifier
Defining MF of input
Fuzzy Rules
Defining Fuzzy Rules
Defuzzifier
Defining MF of output
Test
Test of Fuzzy Classification
System
Figure 4. Classification algorithm
IV. Fuzzy Classification System Design
In this application there is one input and three outputs.
Input variable is α and output variables are 3th, 5th and
7th current harmonic levels. They are defined using
MATLAB Fuzzy Logic Toolbox as shown in figure 5.
After defining Fuzzy Inference System we tested the
system. Finally we shown that 3th, 5th and 7th current
harmonics can be classify by using fuzzy classification.
After classification of harmonics we can design a new
Active Harmonic filter.
Rule1:
If Angle=1 then 3.Harmonic=1 and
5.Harmonic=1 and 7.Harmonic=1
Rule2:
If Angle=2 then 3.Harmonic=2 and
5.Harmonic=2 and 7.Harmonic=2
Rule3:
If Angle=3 then 3.Harmonic=3 and
5.Harmonic=3 and 7.Harmonic=3
Rule18:
If Angle=18 then 3. Harmonic=18 and
5. Harmonic=18 and 7.Harmonic=18.
Figure 5. Definition of angle and harmonic levels
After defining input and output variables we defined also
MF for input variable α and output variables 3th, 5th, 7th
harmonic levels using figure 3. When defining MF of an
angle MFs per 100 will be defined. So optimization has
done for defining of MFs. Similarly when defining MFs
of 3th, 5th and 7th current harmonic levels, harmonic
levels output takes only one value for every 100. As it is
shown in figure 6 variable angle has 18 MFs.
Figure 7. Fuzzy rules
Finally fuzzy classification system will be tested using
Rule Viewer for different α values as shown in figure 8.
Figure 6. MF of angle
3th, 5th and 7th current harmonics as a function of angle
will be decided as “if then” fuzzy rules. There are 18
rules and this rules are defined in Matlab Fuzzy Rules
editor as shown in figure 7.
Figure 8. Rule Viewer of fuzzy classification system
Table 1. Fuzzy system outputs for different angles
Harmonics (%)
Analaysis
Angle
3 th
5 th
7 th
5
15
25
35
45
55
65
75
85
95
105
115
125
135
145
155
165
175
32
31
28
22
15
6
6
15
22
28
31
32
32
31
28
22
15
6
19
15
8
3
9
15
19
19
15
9
3
8
15
19
19
17
13
6
12
8
3
8
12
12
9
3
6
12
12
9
5
5
9
12
12
6
1.Highest
Harmonic
3
3
3
3
3
5
5
5
3
3
3
3
3
3
3
3
3
3,5,7
We can get the fuzzy system outputs for different α
values using matlab rule viewer. The Fuzzy system
outputs for different α values are shown in table 1.
According to this table harmonic degrees of 3th, 5th and
7th current harmonics and highest harmonics can be
determined as a function of angle α.
2.Highest
Harmonic
5
5
5
7
7
7
7
3
5
7
7
7
5
5
5
5
5
3,5,7
3.Highest
Harmonic
7
7
7
5
5
3
3
7
7
5
5
5
7
7
7
7
7
3,5,7
For example, 3th, 5th and 7th current harmonics are
given in table 1 as % for angel 50. If we can measure the
fundamental current (I1) then we can calculate the I3, I5
and I7 harmonic currents as it is shown below.
I3=0,32*I1
I5=0,19*I1
I7=0,12*I1
V. An Active Filter Design
We can calculate also %THD (Total Harmonic
Distortion) using 3th, 5th and 7th current harmonics
which are given in table 1.
3th, 5th and 7th current harmonics are shown in figure 9
as bar graphs.
120



100
2
100
(1)
For example we can calculate %THD for 50 angle using
equation 1;
80
%
 Ih
0 THD =

0
∑
h=2  I1
∞
60
32
40
19
20
12
0
0
0
THD =
(32)
2
+ (19) + (12) = 40
2
2
We can say that if %THD value is high it has to be use a
filter. If we would like to use an Active Filter, we must
find the active filter compansation currents.
1
2
3
4
5
6
7
Harmonics
Figure 9. 3th, 5th and 7th Current Harmonics for angle 50
For the filtering of the 3th, 5th and 7th currents
harmonic, AF has to produce - I3, - I5 and - I7
compansation currents which are shown in figure 10
The proposed fuzzy classification approach has been
successfully applied to classification hormonic distortion
level as a function of α in full-bridge, single-phase
inverters. In addition an improved control algorithm of
the active filter system has been implemented for
harmonic elimination of full-bridge, single-phase inverter
0
-20
1
%
-40
2
3
4
5
-19
6
7
-12
-60
[1] Ned Mohan, Tore M. Undeland and William P.
Robbins , ”Power Electronics Converters, Applications,
and Design” Second Edition, John Wiley & Sons , 1995,
pp.218-219.
-80
-100
-120
-100
Currents
[2] W.R.A. Ibrahim, “Adaptive Neuro-Fuzzy and Expert
Systems For Power Quality Analysis and Prediction of
Abnormal Operation”, Ph.D., Kansas State University,
2001. , pp. 40-44
Figure10. Active filter compansation currents
Figure 11 shows the control scheme of the AF.
According to this figure, pulse angle of the single phase
inverter and fundamental current value are used for
implementation of control scheme. In real time
implementation of the AF fuzzy classification system
plays an impotant role. After classification of 3th, 5th
and 7th current harmonics, 3th, 5th and 7th harmonic
currents can be calculated. In this condition AF
compansation currents can also be calculated. So the
control algorithm of the AF provides reference supply
currents.
=
∼
α I1
α
VII. References
-32
AF
Load
IAF
Calculation
Reference
IAF
Fuzzy
Class.
System
Figure 11. Control scheme of the active filter
VI. Conclusion
This research shows that classification of 3th, 5th and
7th current harmonics and THD in Full-bridge, singlephase inverter using fuzzy classification system is
satisfied.
[3] L.A. Zadeh, “Fuzzy sets,” Information Control,
Vol. 8, 1965, pp.338-353.
[4] Hung T. Nguyen, Elbert A. Walker, A first Course In
Fuzzy Logic, Chapman and Hall / CRC 2000.
VIII. Biographies
Ersen Kuru (1972) received his BS degree in Electrical
and Electronics from Istanbul Technical University of
Turkey in 1995. From 1995 to 1998 he was assistant in
Abant İzzet Baysal University. He received his MS
degree in Electrical and Electronics from University of
Sakarya in 1998. From 1998 to 2002 he was otomation
engineer in Ereğli Iron and Steel Co. His research
interest include design of distributed computer control
systems, Harmonics, SCADA and Fuzzy-logic.
Leyla Kuru (1973) received her degree in Electrical and
Electronics from Istanbul Technical University of
Turkey. From 1995 to 1998 she was assistant in Abant
İzzet Baysal University. She received her MS degree in
Electronics from University of Sakarya in 1998. From
1998 to 2002 She was computer system engineer in
Ereğli Iron and Steel Co. Her research interest include
design of distributed computer control systems, MVS
system,
Etem KÖKLÜKAYA (1955) received his PHD degree
in Electrical and Electronics from Istanbul Technical
University of Turkey in 1990. He is a Associate
Professor in the University of Sakarya. His research
interest include design of distributed computer control
systems, Communications, Harmonics, SCADA,
Biomedical Systems and Fuzzy-logic.